Individual optimization: Mechanisms shaping the optimal reaction norm

In general, optimal reaction norms in heterogeneous populations can be obtained only by iterative numerical procedures (McNamara, 1991; Kawecki and Stearns, 1993). We consider two particular, but biologically plausible and analytically tractable cases of individual optimization to gain insight into the mechanisms which shape the optimal reaction norm of fecundity in relation to an environmental variable or an individual trait. In the first case, we assume that the quality of the environment (e.g. food abundance) or the quality of the individual (e.g. body size) is fixed during its entire life; it may also be a heritable individual trait. In the second case, individual quality is assumed to change randomly such that the probability distribution of quality in the next year is the same for the parent and for her offspring. For these two cases, we obtain analytical expressions for the shape of the optimal reaction norm, which are heuristically interpretable in terms of underlying selective mechanisms. It is shown that better quality may reduce the optimal fecundity. This outcome is particularly likely if better quality increases a fecundity-independent factor of parental survival in a long-lived species with fixed quality. This revised version was published online in July 2006 with corrections to the Cover Date.